2011/07/14 by Chuanming Zong, Zong, Chuanming
Computer Science · Mathematics · #52B20 #52C07 #Advanced Combinatorial Mathematics #Computational Geometry and Mesh Generation #FOS: Mathematics #Metric Geometry (math.MG) #Point processes and geometric inequalities
paper · pdf · doi:10.48550/arxiv.1107.2966
openalex publication_date 2011/07/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In 1980, V.I. Arnold studied the classification problem for convex lattice polygons of given area. Since then this problem and its analogues have been studied by B'ar'any, Pach, Vershik, Liu, Zong and others. Upper bounds for the numbers of non-equivalent ddimensional convex lattice polytopes of given volume or cardinality have been achieved. In this paper, by introducing and studying the unimodular groups acting on convex lattice polytopes, we obtain lower bounds for the number of non-equivalent d-dimensional convex lattice polytopes of bounded volume or given cardinality, which are essentially tight.